In this paper, I ask whether we should see different logical systems as appropriate for different domains (or perhaps in different contexts) and whether this would amount to a form of logical pluralism. One, though not the only, route to this type of position, is via pluralism about truth. Given that truth is central to validity, the commitment the typical truth pluralist has to different notions of truth for different domains may suggest differences regarding validity in those different domains. Indeed, (...) as we’ll see, the differences between the proposed multiple notions of truth are often of a type that is clearly significant in relation to logical features, such as whether or not a constructive notion of truth is at issue. I criticise domain-based logical pluralism. Having done so I introduce a context-based framework that operates with a context-relative notion of validity. I show that this context-based framework can be employed by the domain-specific logical pluralist, but that framework also allows for logical pluralism that does not involve several domains. Different contexts may demand rules of classical logic, where others only justify intuitionistic rules, even when the same domain (e.g. mathematics) is at issue. (shrink)

A distinction is introduced between itemized and non-itemized plural predication. It is argued that a full-fledged system of plural logic is not necessary in order to account for the validity of inferences concerning itemized collective predication. Instead, it is shown how this type of inferences can be adequately dealt with in a first-order logic system, after small modifications on the standard treatment. The proposed system, unlike plural logic, has the advantage of preserving completeness. And (...) as a result, inferences such as ‘Dick and Tony emptied the bottle, hence Tony and Dick emptied the bottle’ are shown to be first-order. (shrink)

We note that a plural version of logicism about arithmetic is suggested by the standard reading of Hume's Principle in terms of `the number of Fs/Gs'. We lay out the resources needed to prove a version of Frege's principle in plural, rather than second-order, logic. We sketch a proof of the theorem and comment philosophically on the result, which sits well with a metaphysics of natural numbers as plural properties.

In recent decades, plural logic has established itself as a well-respected member of the extensions of first-order classical logic. In the present paper, I draw attention to the fact that among the examples that are commonly given in order to motivate the need for this new logical system, there are some in which the elements of the plurality in question are internally singularized (e.g. ‘Whitehead and Russell wrote Principia Mathematica’), while in others they are not (e.g. ‘Some (...) philosophers wrote Principia Mathematica’). Then, building on previous work, I point to a subsystem of plural logic in which inferences concerning examples of the first type can be adequately dealt with. I notice that such a subsystem (here called ‘discrete plural logic’) is in reality a mere variant of first-order logic as standardly formulated, and highlight the fact that it is axiomatizable while full plural logic is not. Finally, I urge that greater attention be paid to discrete plural logic and that discrete plurals are not used in order to motivate the introduction of full-fledged plural logic—or, at least, not without remarking that they can also be adequately dealt with in a considerably simpler system. (shrink)

Plural expressions found in natural languages allow us to talk about many objects simultaneously. Plural logic — a logical system that takes plurals at face value — has seen a surge of interest in recent years. This book explores its broader significance for philosophy, logic, and linguistics. What can plural logic do for us? Are the bold claims made on its behalf correct? After introducing plural logic and its main applications, the book (...) provides a systematic analysis of the relation between this logic and other theoretical frameworks such as set theory, mereology, higher-order logic, and modal logic. The applications of plural logic rely on two assumptions, namely that this logic is ontologically innocent and has great expressive power. These assumptions are shown to be problematic. The result is a more nuanced picture of plural logic's applications than has been given thus far. Questions about the correct logic of plurals play a central role in the final chapters, where traditional plural logic is rejected in favor of a "critical" alternative. The most striking feature of this alternative is that there is no universal plurality. This leads to a novel approach to the relation between the many and the one. In particular, critical plural logic paves the way for an account of sets capable of solving the set-theoretic paradoxes. (shrink)

It is often assumed that pluralities are rigid, in the sense of having all and only their actual members necessarily. This assumption is operative in standard approaches to modal plural logic. I argue that a sceptical approach towards the assumption is warranted.

This paper replies to Himmelreich's ‘The Paraphrase Argument Against Collective Actions’ [2017], which presents three putative counterexamples to the multiple agents analysis of plural action sentences. The paper shows that the argument from the first example, the discursive dilemma, fails because it relies crucially on a simplification of the target analysis, and that the others don't bear on the question because they turn out on examination to be about individual rather than group action sentences.

This volume brings together new work on the logic and ontology of plurality and a range of recent articles exploring novel applications to natural language semantics. The contributions in this volume in particular investigate and extend new perspectives presented by plural logic and non-standard mereology and explore their applications to a range of natural language phenomena. Contributions by P. Aquaviva, A. Arapinis, M. Carrara, P. McKay, F. Moltmann, O. Linnebo, A. Oliver and T. Smiley, T. Scaltsas, P. (...) Simons, and B.-Y. Yi . (shrink)

Noun phrases with overt determiners, such as <i>some apples</i> or <i>a quantity of milk</i>, differ from bare noun phrases like <i>apples</i> or <i>milk</i> in their contribution to aspectual composition. While this has been attributed to syntactic or algebraic properties of these noun phrases, such accounts have explanatory shortcomings. We suggest instead that the relevant property that distinguishes between the two classes of noun phrases derives from two modes of existential quantification, one of which holds the values of a variable fixed (...) throughout a quantificational context while the other allows them to vary. Inspired by Dynamic Plural Logic and Dependence Logic, we propose Plural Predicate Logic as an extension of Predicate Logic to formalize this difference. We suggest that temporal <i>for</i>-adverbials are sensitive to aspect because of the way they manipulate quantificational contexts, and that analogous manipulations occur with spatial <i>for</i>-adverbials, habituals, and the quantifier <i>all</i>. (shrink)

In To be is to be the object of a possible act of choice the authors defended Boolos’ thesis that plural quantification is part of logic. To this purpose, plural quantification was explained in terms of plural reference, and a semantics of plural acts of choice, performed by an ideal team of agents, was introduced. In this paper, following that approach, we develop a theory of concepts that—in a sense to be explained—can be labeled as (...) a theory of logical concepts. Within this theory, we propose a new logicist approach to natural numbers. Then, we compare our logicism with Frege’s traditional logicism. (shrink)

In linguistics, the dominant approach to the semantics of plurals appeals to mereology. However, this approach has received strong criticisms from philosophical logicians who subscribe to an alternative framework based on plural logic. In the first part of the article, we offer a precise characterization of the mereological approach and the semantic background in which the debate can be meaningfully reconstructed. In the second part, we deal with the criticisms and assess their logical, linguistic, and philosophical significance. We (...) identify four main objections and show how each can be addressed. Finally, we compare the strengths and shortcomings of the mereological approach and plural logic. Our conclusion is that the former remains a viable and well-motivated framework for the analysis of plurals. (shrink)

This paper defends 'plural reference', the view that definite plurals refer to several individuals at once, and it explores how the view can account for a range of phenomena that have been discussed in the linguistic literature.

In 1903, in _The Principles of Mathematics_ (_PoM_), Russell endorsed an account of classes whereupon a class fundamentally is to be considered many things, and not one, and used this thesis to explicate his first version of a theory of types, adding that it formed the logical justification for the grammatical distinction between singular and plural. The view, however, was short-lived; rejected before _PoM_ even appeared in print. However, aside from mentions of a few misgivings, there is little evidence (...) about why he abandoned this view. In this paper, I speculate as to what those reasons were, and evaluate them in light of recent work and interest in plural logic. (shrink)

A plurality or plural object is a single object that is also many, and pluralitism is the thesis that there is such an object. This paper argues that pluralitism and closely related theses (e.g., the many-one identity thesis and the composition as identity thesis) violate logic. To do so, it formulates an approach to the logic and semantics of plural constructions that results in plural logic and relates treatments of plural constructions to accounts (...) of natural number. And it gives a critical examination of Frege’s views of numbers and plural constructions, and sketches the view of plural constructions as devices for talking about the many (as such), and an account of natural numbers as properties of a special kind, plural properties. (shrink)

According to the singular conception of reality, there are objects and there are singular properties, i.e. properties that are instantiated by objects separately. It has been argued that semantic considerations about plurals give us reasons to embrace a plural conception of reality. This is the view that, in addition to singular properties, there are plural properties, i.e. properties that are instantiated jointly by many objects. In this article, I propose and defend a novel semantic account of plurals which (...) dispenses with plural properties and thus undermines the semantic argument in favor of the plural conception of reality. (shrink)

According to ‘Strong Composition as Identity’, if an entity is composed of a plurality of entities, it is identical to them. As it has been argued in the literature, SCAI appears to give rise to some serious problems which seem to suggest that SCAI-theorists should take their plural quantifier to be governed by some ‘weak’ plural comprehension principle and, thus, ‘exclude’ some kinds of pluralities from their plural ontology. The aim of this paper is to argue that, (...) contrary to what may appear at first sight, the assumption of a weak plural comprehension principle is perfectly compatible with plural logic and the common uses of plural quantification. As I aim to show, SCAI-theorists can simply claim that their theory must be understood as formulated by means of the most ‘joint-carving’ plural quantifier, thus leaving open the possibility of other, less joint-carving, ‘unrestricted’ plural quantifiers. In the final part of the paper I will also suggest that SCAI-theorists should not only allow for singular quantification over pluralities of entities, but also for plural quantification over ‘super-pluralities’ of entities. (shrink)

It is well-known that in the fifth of his Cartesian Meditations, Husserl puts forth a theory of intersubjectivity. Most commentators of Husserl have read his Cartesian Meditations as presenting a theory of intersubjectivity whose basis is empathy, in the form of a process of constituting the sense of “other” in one’s own experience, as the primary origin of the intersubjective layer of experience. In this paper, I claim that the structure of intersubjectivity as Husserl presents it in the Cartesian Meditations (...) is articulated as being governed by a logic of parts and wholes rather than that of a phenomenology of empathy, and that the articulation of this logic demonstrates that the transcendental ego is intrinsically intersubjective. My main philosophical claim in this regard is that the way Husserl’s account of transcendental empathy unfolds in the Cartesian Meditations implies a prior fundamental mereological structure of which the individual transcendental ego is only a part. That is, the transcendental ego has an eidetic a-priori intersubjective structure, in the sense of being a moment of an intersubjectively structured transcendental whole. In this sense, rather than being a singulare tantum, it is more fitting to say that transcendental subjectivity is actually a plurale tantum. (shrink)

The first aim of this paper is to prove a topological completeness theorem for a weak version of Stalnaker’s logic KB of knowledge and belief. The weak version of KB is characterized by the assumption that the axioms and rules of KB have to be satisfied with the exception of the axiom (NI) of negative introspection. The proof of a topological completeness theorem for weak KB is based on the fact that nuclei (as defined in the framework of point-free (...) topology) give rise to a profusion of topological belief operators that are compatible with the familiar topological knowledge operator. Thereby a canonical topological model for weak KB can be constructed. For this canonical model a truth lemma for the K and B holds such that a completeness theorem for KB can be proved in the familiar way. The second aim of this paper is to show that the topological interpretation of knowledge K comes along with a complete Heyting algebra of belief operators B that all fit the knowledge operator K in the sense that the pairs (K, B) satisfy all axioms of weak KB. This amounts to a pluralistic relation between knowledge and belief: Knowledge does not fully determine belief, rather it designs a conceptual space for belief operators where different (competing) belief operators coexist. (shrink)

This chapter is concerned with plural discourse in the grammatical sense. The goal of the chapter is to urge the value of the event analysis of the matrix of action sentences in thinking about logical form in plural discourse about action. Among the claims advanced are that: -/- 1. The ambiguity between distributive and collective readings of plural action sentences is not lexical ambiguity, either in the noun phrase (NP) or in the verb phrase (VP), but an (...) ambiguity tracing to the scope of the event quantifier introduced by the action verb. 2. This allows us to analyze collective action sentences in a way that commits us only to individual agents acting when we say that groups act, without denying that there are groups as such or that we talk about them as such. 3. Intermediate readings, that seem to be neither purely distributive nor purely collective, can be explained in terms of the same apparatus. (shrink)

Mereological universalists and nihilists disagree on the conditions for composition. In this paper, we show how this debate is a function of one’s chosen semantics for plural quantifiers. Debating mereologists have failed to appreciate this point because of the complexity of the debate and extraneous theoretical commitments. We eliminate this by framing the debate between universalists and nihilists in a formal model where these two theses about composition are contradictory. The examination of the two theories in the model brings (...) clarity to a debate in which opponents frequently talk past one another. With the two views stated precisely, our investigation reveals the dependence of the mereologists’ ontological commitments on the semantics of plural quantifiers. Though we discuss the debate with respect to a simplified and idealized model, the insights provided will make more complex debates on composition more productive and deflationist criticisms of the debate less substantial. (shrink)

In western philosophy and beyond, a tension between pluralism and monism has sparked many developments and debates. Pluralism of norms, of forms of knowledge, of aesthetic and moral values, of interests etc. has often been pitted against monism. Monism usually implies a hierarchical order of such norms etc. After having traced the origin of this tension between pluralism and monism in ancient tragedy and philosophy, I’m asking in this article whether a rejection of monism and embrace of pluralism necessarily raises (...) the specter of inconsistency and contradiction. The threat of inconsistency need not be associated with pluralism as even with regard to logic an argument can be made for a ‘multiplicity of logics’, as van Lambalgen and Stenning argue in several places. They refer to the varieties in reasoning that can be observed in humans and which are partly due to there being ‘dual systems’ of reasoning: System 1 processes information fast, automatized, and emotional, while System 2 is rather slow, more deliberative, and more rational. In contrast to a widely held view, the authors argue that System 1 processing is not without logic, even though it is a different form of logic from System 2. In addition, the multiplicity of logics they discuss is related to the multiple semantics required for distinct domains of reasoning. This perspective raises the subsequent question how this pluralism can be available while maintaining consistency, how should the available options be configured or related to each other? In the remainer of this chapter I’m addressing several such options for configurating pluralism like: non-foundational pluralism and foundational pluralism, moderate or temporary pluralism, antagonistic pluralism, incompatible pluralism, incommensurable pluralism, ‘Anything goes’ pluralism, complementary pluralism, integrative pluralism, and interactive pluralism. The discussion and examples of these options show that irrespective of its domain, the encounter with different configurations of pluralism shows how some forms of pluralism are likely to be productive, whereas others are less so - which is an important lesson given the prominent pluralism of pluralisms in philosophy and beyond. (shrink)

I argue that Composition as Identity blocks the plural version of Cantor's Theorem, and that therefore the plural version of Cantor's Theorem can no longer be uncritically appealed to. As an example, I show how this result blocks a recent argument by Hawthorne and Uzquiano.

Neo-Fregean approaches to set theory, following Frege, have it that sets are the extensions of concepts, where concepts are the values of second-order variables. The idea is that, given a second-order entity $X$, there may be an object $\varepsilon X$, which is the extension of X. Other writers have also claimed a similar relationship between second-order logic and set theory, where sets arise from pluralities. This paper considers two interpretations of second-order logic—as being either extensional or intensional—and whether (...) either is more appropriate for this approach to the foundations of set theory. Although there seems to be a case for the extensional interpretation resulting from modal considerations, I show how there is no obstacle to starting with an intensional second-order logic. I do so by showing how the $\varepsilon$ operator can have the effect of “extensionalizing” intensional second-order entities. (shrink)

In Lewis reconstructs set theory using mereology and plural quantification (MPQ). In his recontruction he assumes from the beginning that there is an infinite plurality of atoms, whose size is equivalent to that of the set theoretical universe. Since this assumption is far beyond the basic axioms of mereology, it might seem that MPQ do not play any role in order to guarantee the existence of a large infinity of objects. However, we intend to demonstrate that mereology and (...) class='Hi'>plural quantification are, in some ways, particularly relevant to a certain conception of the infinite. More precisely, though the principles of mereology and plural quantification do not guarantee the existence of an infinite number of objects, nevertheless, once the existence of any infinite object is admitted, they are able to assure the existence of an uncountable infinity of objects. So, ifMPQ were parts of logic, the implausible consequence would follow that, given a countable infinity of individuals, logic would be able to guarantee an uncountable infinity of objects. (shrink)

This reviews, motivates, and extends the event analysis of action sentences and shows how it explains the compositionally of adverbial modification of action verbs and event verbs more generally. It includes a treatment of intensional adverbs like 'intentionally' and how it can be extended to the collective reading of plural action sentences.

At A71/B96–7 Kant explains that singular judgements are ‘special’ because they stand to the general ones as Einheit to Unendlichkeit. The reference to Einheit brings to mind the category of unity and hence raises a spectre of circularity in Kant’s explanation. I aim to remove this spectre by interpreting the Einheit-Unendlichkeit contrast in light of the logical distinctions among universal, particular and singular judgments shared by Kant and his logician predecessors. This interpretation has a further implication for resolving a controversy (...) over the correlation between the logical moments of quantity (universal, particular, singular) and the categorial ones (unity, plurality, totality). (shrink)

In almost all of his early works Gilles Deleuze is concerned with one and the same problem: the problem of genesis. In response to this problem, Deleuze argues for a system of heterogenesis. In this article, I argue that Deleuze’s system of heterogenesis operates on three levels: (1) the differential multiplicity of virtual Ideas; (2) the implied multiplicity of intensive dramas; (3) the extensive and qualitative diversity of actual concepts. As I hope to show, the relation between these three levels (...) can be explained in terms of the logic of expression that Deleuze develops in 'Expressionism in Philosophy: Spinoza.' In this way, I hope to gain clarity without losing nuance. The rather technical and abstract language of expression will become more concrete and understandable when it is understood in terms of intensive dramas, virtual Ideas and actual concepts. At the same time, the three levels of expression make it possible to show how these notions are interlinked. Accordingly, this article is divided in four parts. In the first part, I will explain how Deleuze takes up Kant’s discovery of the principle of difference as a reaction against the model of representation. The second part focuses on the two multiplicities (virtual Ideas and intensive dramas) that produce diversity (actual concepts). In the third part, these two multiplicities are linked to each other with the help of the logic of expression that Deleuze derives from Spinoza. The fourth, concluding part will connect the logic of expression to the complex dynamic of difference and repetition. (shrink)

Recently there is a renewed academic interest in religion bringing it back on the global political agenda. Religion in the post modern global order is fast emerging as a new organizing principle in the face of multi-polarity, trans-nationality and sweeping pluralisation of peoples. Contrary to the secularist self believe, the modern has failed to take over the tradition including religion. Rather a logical opposite seems to be happening, questioning the very presumptions of the modernity project. The present paper is a (...) narrative on this creative tension in the religious modern and post modern. The paper is crafted into four sections. First section seeks to pin down the genesis of “religious” in the search for social order and consciousness beyond the material world. Second section deals with the unfolding of enlightenment project and its manifest consequence with the birth of secularism master theory. Third section delves deep into the immediate Indian religious lived experiences under foreign rule up to the sweeping spell of globalisation. Fourth and last part of the essay makes a case for universality of a multicultural world and religious secularism. (shrink)

In this paper I try to answer four basic questions: (1) How the concept of God is to be represented? (2) Are there any logical principles governing it? (3) If so, what kind of logic lies behind them? (4) Can there be a logic of the concept of God? I address them by presenting a formal-logical account to the concept of God. I take it as a methodological desideratum that this should be done within the simplest existing logical (...) formalism. I start with first-order logic (FOL) with identity, and then show that its simplest modal extension (SQML, or the simplest quantified modal logic) is enough for us to formalize a minimally satisfactory theory of the concept of God. I focus exclusively on the monotheistic concept of God. (shrink)

In this paper I aim to defend a first‐order non‐discriminating property view concerning existence. The version of this view that I prefer is based on negative (or a specific neutral) free logic that treats the existence predicate as first‐order logical predicate. I will provide reasons why such a view is more plausible than a second‐order discriminating property view concerning existence and I will also discuss four challenges for the proposed view and provide solutions to them.

In this paper we begin categorizing a plurality of possible worlds on the basis of permitting or not permitting ontologically different things to be causally connected. We build the work on the dual principle that all universes are causally closed either because no universe causes anything outside itself or because no universe has anything in it that is caused by another universe.

According to tradition, logic is normative for reasoning. According to many contemporary philosophers of logic, there is more than one correct logic. What is the relationship between these two strands of thought? This paper makes two claims. First, logic is doubly normative for reasoning because, in addition to constraining the combinations of beliefs that we may have, logic also constrains the methods by which we may form them. Second, given that logic is doubly normative (...) for reasoning, a wide array of logical pluralisms are inconsistent with the normativity of logic as they entail contradictory claims about how agents ought to reason. Thus, if logic is normative for reasoning, these pluralisms are untenable. (shrink)

It will be shown in this article that an ontological approach for some problems related to the interpretation of Quantum Mechanics (QM) could emerge from a re-evaluation of the main paradox of early Greek thought: the paradox of Being and non-Being, and the solutions presented to it by Plato and Aristotle. More well known are the derivative paradoxes of Zeno: the paradox of motion and the paradox of the One and the Many. They stem from what was perceived by classical (...) philosophy to be the fundamental enigma for thinking about the world: the seemingly contradictory results that followed from the co-incidence of being and non-being in the world of change and motion as we experience it, and the experience of absolute existence here and now. The most clear expression of both stances can be found, again following classical thought, in the thinking of Heraclitus of Ephesus and Parmenides of Elea. The problem put forward by these paradoxes reduces for both Plato and Aristotle to the possibility of the existence of stable objects as a necessary condition for knowledge. Hence the primarily ontological nature of the solutions they proposed: Plato’s Theory of Forms and Aristotle’s metaphysics and logic. Plato’s and Aristotle’s systems are argued here to do on the ontological level essentially the same: to introduce stability in the world by introducing the notion of a separable, stable object, for which a ‘principle of contradiction’ is valid: an object cannot be and not-be at the same place at the same time. So it becomes possible to forbid contradiction on an epistemological level, and thus to guarantee the certainty of knowledge that seemed to be threatened before. After leaving Aristotelian metaphysics, early modern science had to cope with these problems: it did so by introducing “space” as the seat of stability, and “time” as the theater of motion. But the ontological structure present in this solution remained the same. Therefore the fundamental notion ‘separable system’, related to the notions observation and measurement, themselves related to the modern concepts of space and time, appears to be intrinsically problematic, because it is inextricably connected to classical logic on the ontological level. We see therefore the problems dealt with by quantum logic not as merely formal, and the problem of ‘non-locality’ as related to it, indicating the need to re-think the notions system, entity, as well as the implications of the operation ‘measurement’, which is seen here as an application of classical logic (including its ontological consequences) on the material world. (shrink)

Abstract. Traditional epistemology of knowledge and belief can be succinctly characterized as JTB-epistemology, i.e., it is characterized by the thesis that knowledge is justified true belief. Since Gettier’s trail-blazing paper of 1963 this account has become under heavy attack. The aim of is paper is to study the Gettier problem and related issues in the framework of topological epistemic logic. It is shown that in the framework of topological epistemic logic Gettier situations necessarily occur for most topological models (...) of knowledge and belief. On the other hand, there exists a special class of topological models (based on so called nodec spaces) for which traditional JTB-epistemology is valid. Further, it is shown that for each topological model of Stalnaker’s combined logic KB of knowledge and belief a canonical JTB-model (its JTB-doppelganger) can be constructed that shares many structural properties with the original model but is free of Gettier situations. The topological model and its JTB-doppelganger both share the same justified belief operator and have very similar knowledge operators. Seen from a somewhat different perspective, the JTB-account of epistemology amounts to a simplification of a more general epistemological account of knowledge and belief that assumes that these two concepts may differ in some cases. The JTB-account of knowledge and belief assumes that the epistemic agent’s cognitive powers are rather large. Thereby in the JTB-epistemology Gettier cases do not occur. Eventually, it is shown that for all topological models of Stalnaker’s KB-logic Gettier situations are topologically characterized as nowhere dense situations. This entails that Gettier situations are epistemologically invisible in the sense that they can neither be known nor believed with justification with respect to the knowledge operator and the belief operator of the models involved. (shrink)

I like the view that the fundamental facts are logically simple, not complex. However, some universal generalizations and negations may appear fundamental, because they cannot be explained by logically simple facts about particulars. I explore a natural reply: those universal generalizations and negations are true because certain logically simple facts—call them —are the fundamental facts. I argue that this solution is only available given some metaphysical frameworks, some conceptions of metaphysical explanation and fundamentality. It requires a ‘fitting’ framework, according to (...) which metaphysical theories explain the aptness of representations in terms of how things are fundamentally. Fitting frameworks conceive of the fundamental facts as those that are metaphysically ‘real’; call them the ‘facts-in-reality’. Moreover, we must take as primary a plural notion of the facts-in-reality, not the singular notion of a fact-in-reality. By contrast, a metaphysics that grounds facts is incompatible with my strategy for keeping the fundamental facts logically simple. (shrink)

According to the so-called strong variant of Composition as Identity (CAI), the Principle of Indiscernibility of Identicals can be extended to composition, by resorting to broadly Fregean relativizations of cardinality ascriptions. In this paper we analyze various ways in which this relativization could be achieved. According to one broad variety of relativization, cardinality ascriptions are about objects, while concepts occupy an additional argument place. It should be possible to paraphrase the cardinality ascriptions in plural logic and, as a (...) consequence, relative counting requires the relativization either of quantifiers, or of identity, or of the is one of relation. However, some of these relativizations do not deliver the expected results, and others rely on problematic assumptions. In another broad variety of relativization, cardinality ascriptions are about concepts or sets. The most promising development of this approach is prima facie connected with a violation of the so-called Coreferentiality Constraint, according to which an identity statement is true only if its terms have the same referent. Moreover - even provided that the problem with coreferentiality can be fixed - the resulting analysis of cardinality ascriptions meets several difficulties. (shrink)

The emerging field of quantum mereology considers part-whole relations in quantum systems. Entangled quantum systems pose a peculiar problem in the field, since their total states are not reducible to that of their parts. While there exist several established proposals for modelling entangled systems, like monistic holism or relational holism, there is considerable unclarity, which further positions are available. Using the lambda operator and plural logic as formal tools, we review and develop conceivable models and evaluate their consistency (...) and distinctness. The main result is an exhaustive taxonomy of six distinct and precise models that both provide information about the mereological features as well as about the entangled property. The taxonomy is well-suited to serve as the basis for future systematic investigations. (shrink)

Composition as Identity is the view that an object is identical to its parts taken collectively. I elaborate and defend a theory based on this idea: composition is a kind of identity. Since this claim is best presented within a plural logic, I develop a formal system of plural logic. The principles of this system differ from the standard views on plural logic because one of my central claims is that identity is a relation (...) which comes in a variety of forms and only one of them obeys substitution unrestrictedly. I justify this departure from orthodoxy by showing some problems which result from attempts to avoid inconsistencies within plural logic by means of postulating other non-singular terms besides plural terms. Thereby, some of the main criticisms raised against Composition as Identity can be addressed. Further, I argue that the way objects are arranged is relevant with respect to the question which object they compose, i.e. to which object they are identical to. This helps to meet a second group of arguments against Composition as Identity. These arguments aim to show that identifying composite objects on the basis of the identity of their parts entails, contrary to our common sense view, that rearranging the parts of a composite object does not leave us with a different object. Moreover, it allows us to carve out the intensional aspects of Composition as Identity and to defend mereological universalism, the claim that any objects compose some object. Much of the pressure put on the latter view can be avoided by distinguishing the question whether some objects compose an object from the question what object they compose. Eventually, I conclude that Composition as Identity is a coherent and plausible position, as long as we take identity to be a more complex relation than commonly assumed. (shrink)

We will explicate Cantor’s principle of set existence using the Gödelian intensional notion of absolute provability and John Burgess’ plural logical concept of set formation. From this Cantorian Comprehension principle we will derive a conditional result about the question whether there are any absolutely unprovable mathematical truths. Finally, we will discuss the philosophical significance of the conditional result.

“Slingshot Arguments” are a family of arguments underlying the Fregean view that if sentences have reference at all, their references are their truth-values. Usually seen as a kind of collapsing argument, the slingshot consists in proving that, once you suppose that there are some items that are references of sentences (as facts or situations, for example), these items collapse into just two items: The True and The False. This dissertation treats of the slingshot dubbed “Gödel’s slingshot”. Gödel argued that there (...) is a deep connection between these arguments and definite descriptions. More precisely, according to Gödel, if one adopts Russell’s interpretation of definite descriptions (which clashes with Frege’s view that definite descriptions are singular terms), it is possible to evade the slingshot. We challenge Gödel’s view in two manners, first by presenting a slingshot even with a Russellian interpretation of definite descriptions and second by presenting a slingshot even when we change from singular terms to plural terms in the light of new developments of the so-called Plural Logic. The text is divided in three chapters, in the first, we present the discussion between Russell and Frege regarding definite descriptions, in the second, we present Gödel’s position and reconstructions of Gödel’s argument and in the third we prove our slingshot argument for Plural Logic. In light of these results we conclude that we can maintain the validity of slingshot arguments even within a Russellian interpretation of definite descriptions or in the context of Plural Logic. (shrink)

I argue that absolutism, the view that absolutely unrestricted quantification is possible, is to blame for both the paradoxes that arise in naive set theory and variants of these paradoxes that arise in plural logic and in semantics. The solution is restrictivism, the view that absolutely unrestricted quantification is not possible. -/- It is generally thought that absolutism is true and that restrictivism is not only false, but inexpressible. As a result, the paradoxes are blamed, not on illicit (...) quantification, but on the logical conception of set which motivates naive set theory. The accepted solution is to replace this with the iterative conception of set. -/- I show that this picture is doubly mistaken. After a close examination of the paradoxes in chapters 2--3, I argue in chapters 4 and 5 that it is possible to rescue naive set theory by restricting quantification over sets and that the resulting restrictivist set theory is expressible. In chapters 6 and 7, I argue that it is the iterative conception of set and the thesis of absolutism that should be rejected. (shrink)

Featured course on "Dynamic Semantics" at NASSLLI 2016. Day 5: Quantification. Abstract: In discourse, quantifiers can function as antecedents or anaphors. We analyze a sample discourse in Dynamic Plural Logic (DPlL, van den Berg 1993, 1994), which represents not only current discourse referents, but also current relations by means of plural information states. This makes it possible to analyze quantification as structured discourse reference. Finally, the DPlL analysis is transposed into Update with Centering, to simplify the formalism (...) and relate quantification to earlier discussion in the course. (shrink)

Composition as identity, as I understand it, is a theory of the composite structure of reality. The theory’s underlying logic is irreducibly plural; its fundamental primitive is a generalized identity relation that takes either plural or singular arguments. Strong versions of the theory that incorporate a generalized version of the indiscernibility of identicals are incompatible with the framework of plural logic, and should be rejected. Weak versions of the theory that are based on the idea (...) that composition is merely analogous to identity are too weak to be interesting, lacking in metaphysical consequence. I defend a moderate version according to which composition is a kind of identity, and argue that the difference is metaphysically substantial, not merely terminological. I then consider whether the notion of generalized identity, though fundamental, can be elucidated in modal terms by reverse engineering Hume’s Dictum. Unfortunately, for realists about possible worlds, such as myself,... (shrink)

There has been much work on ontological dependence in recent literature. However, relatively little of it has been dedicated to the ways in which individual physical objects may depend on other distinct, non-overlapping objects. This paper gives several examples of such object-dependence and distinguishes between different types of it. The paper also introduces and refines the notion of an n-tet. N-tets (typically) occur when there are object-dependence relations between n objects. I claim that the identity (or, rather, what I call (...) the n-dentity) conditions for n-tets are not grounded in the individual identity conditions of each of the n objects, but instead are metaphysically basic. The paper then briefly discusses some ramifications of accepting object-dependence (and n-tets) on the philosophy of biology, ethics, and logic. (shrink)

Orthodoxy holds that there is a determinate fact of the matter about every arithmetical claim. Little argument has been supplied in favour of orthodoxy, and work of Field, Warren and Waxman, and others suggests that the presumption in its favour is unjustified. This paper supports orthodoxy by establishing the determinacy of arithmetic in a well-motivated modal plural logic. Recasting this result in higher-order logic reveals that even the nominalist who thinks that there are only finitely many things (...) should think that there is some sense in which arithmetic is true and determinate. (shrink)

We can introduce singular terms for ordered pairs by means of an abstraction principle. Doing so proves useful for a number of projects in the philosophy of mathematics. However there is a question whether we can appeal to the abstraction principle in good faith, since a version of the Caesar Problem can be generated, posing the worry that abstraction fails to introduce expressions which refer determinately to the requisite sort of object. In this short paper I will pose the difficulty, (...) and then propose a solution. (shrink)

We can introduce singular terms for ordered pairs by means of an abstraction principle. Doing so proves useful for a number of projects in the philosophy of mathematics. However there is a question whether we can appeal to the abstraction principle in good faith, since a version of the Caesar Problem can be generated, posing the worry that abstraction fails to introduce expressions which refer determinately to the requisite sort of object. In this note I will pose the difficulty, and (...) then propose a solution. Since my solution appeals to a plausible constraint on the introduction of new expressions to a language, it is of interest independently of the particular case of terms for pairs. Since these provide the occasion for discussion we should nonetheless review the use of abstraction for pairs before the argumentative business of the paper commences. (shrink)